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Homework Help: Bernoulli's Equation Prob?

  1. Jan 29, 2008 #1
    [SOLVED] Bernoulli's Equation Prob?

    1. The problem statement, all variables and given/known data
    Water emerges from a faucet of diameter 'd' in steady, near vertical flow with speed 'v'. Show that the diameter of the falling water column is given by D = d[v^2/(v^2+2gh)]^(1/4), were 'h' is the distance below the faucet.

    2. Relevant equations
    I'm not positive where to start but I think Bernoulli's Equation may have something to do with it:

    pressure+.5(density)(velocity)^2 + (density)(gravity)(height) = pressure+.5(density)(velocity)^2 + (density)(gravity)(height)

    maybe the conservation of mass plays a role:
    velocity * area = velocity * area

    3. The attempt at a solution
    I'm terrible at deriving equations. Once I get started I can usually take off but I need that first little push to get me goin. Looking at this problem I see we have the initial diameter, and initial velocity. The water falls due to the acceleration of gravity, creating a higher velocity, and thus a smaller area due to the conservation of mass eqn. That all makes sense to me but I don't really see where I can make any equations out of it. Maybe this is wrong, I need a good understanding of what it happening before I can dive in and try to create the proof.
  2. jcsd
  3. Jan 30, 2008 #2


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    Homework Helper

    use this relationship

    and consider the water to be in free fall in order to determine the velocity of the water when it has fallen through a height h below the fuacet.
  4. Feb 4, 2008 #3
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